Identification of a crack in a beam based on the finite element method of a B-spline wavelet on the interval

2006 ◽  
Vol 296 (4-5) ◽  
pp. 1046-1052 ◽  
Author(s):  
J.W. Xiang ◽  
X.F. Chen ◽  
B. Li ◽  
Y.M. He ◽  
Z.J. He
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
The Finite Element Method ◽  
Spline Wavelet ◽  
B Spline ◽  
Element Method

Generation and Modification of Non-Uniform B-Spline Surface Approximations to PDE Surfaces Using the Finite Element Method

1990 ◽  
Author(s):  
Joanna M. Brown ◽  
Malcolm I. G. Bloor ◽  
M. Susan Bloor ◽  
Michael J. Wilson
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Spline Approximation ◽  
The Finite Element Method ◽  
B Spline ◽  
B Splines ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Spline Basis ◽  
Element Method

Abstract A PDE surface is generated by solving partial differential equations subject to boundary conditions. To obtain an approximation of the PDE surface in the form of a B-spline surface the finite element method, with the basis formed from B-spline basis functions, can be used to solve the equations. The procedure is simplest when uniform B-splines are used, but it is also feasible, and in some cases desirable, to use non-uniform B-splines. It will also be shown that it is possible, if required, to modify the non-uniform B-spline approximation in a variety of ways, using the properties of B-spline surfaces.

scholarly journals About the B-spline wavelet discrete-continual finite element method of the local plate analysis

Vestnik MGSU ◽  
2021 ◽  
pp. 666-675
Author(s):  
Pavel A. Akimov ◽  
Marina L. Mozgaleva ◽  
Taymuraz B. Kaytukov
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Analytical Solution ◽  
Element Approximation ◽  
Plate Material ◽  
Basic Direction ◽  
Spline Wavelet ◽  
B Spline ◽  
Plate Analysis ◽  
Element Method

Introduction. This distinctive paper addresses the local semi-analytical solution to the problem of plate analysis. Isotropic plates featuring the regularity (constancy) of physical and geometric parameters (modulus of elasticity of the plate material, Poisson’s ratio of the plate material, dimensions of the cross section of the plate) along one direction (dimension) are under consideration. This direction is conventionally called the basic direction. Materials and methods. The B-spline wavelet discrete-continual finite element method (DCFEM) is used. The initial operational formulation of the problem was constructed using the theory of distribution and the so-called method of extended domain, proposed by Prof. Alexander B. Zolotov. Results. Some relevant issues of construction of normalized basis functions of the B-spline are considered; the technique of approximation of corresponding vector functions and operators within DCFEM is described. The problem remains continual if analyzed along the basic direction, and its exact analytical solution can be obtained, whereas the finite element approximation is used in combination with a wavelet analysis apparatus in respect of the non-basic direction. As a result, we can obtain a discrete-continual formulation of the problem. Thus, we have a multi-point (in particular, two-point) boundary problem for the first-order system of ordinary differential equations with constant coefficients. A special correct analytical method of solving such problems was developed, described and verified in the numerous papers of the co-authors. In particular, we consider the simplest sample analysis of a plate (rectangular in plan) fixed along the side faces exposed to the influence of the load concentrated in the center of the plate. Conclusions. The solution to the verification problem obtained using the proposed version of wavelet-based DCFEM was in good agreement with the solution obtained using the conventional finite element method (the corresponding solutions were constructed with and without localization; these solutions almost completely coincided, while the advantages of the numerical-analytical approach were quite obvious). It is shown that the use of B-splines of various degrees within wavelet-based DCFEM leads to a significant reduction in the number of unknowns.

101 On fracture analysis using B-spline wavelet finite element method

2008 ◽  
Vol 2008.46 (0) ◽  
pp. 1-2
Author(s):  
Yuichi SUGIMOTO ◽  
Satoyuki TANAKA ◽  
Hiroshi OKADA ◽  
Masahiko FUJIKUBO ◽  
Shigenobu OKAZAWA
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Fracture Analysis ◽  
Spline Wavelet ◽  
B Spline ◽  
Wavelet Finite Element Method ◽  
Wavelet Finite Element ◽  
Element Method

B-Spline Wavelet-Based Finite Element Vibration Analysis of Composite Pipes with Internal Surface Defects of Different Geometries

2017 ◽  
Vol 17 (04) ◽  
pp. 1750051 ◽  
Author(s):  
Wasiu A. Oke ◽  
Yehia A. Khulief
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Vibration Analysis ◽  
Surface Defects ◽  
Internal Surface ◽  
Spline Wavelet ◽  
B Spline ◽  
Composite Pipe ◽  
Composite Pipes ◽  
Element Method

The vibration analysis of composite pipes with internal wall defects due to erosion-induced surface degradation is investigated. The surface defects are treated as discontinuities. The geometry of the discontinuity is permitted to vary within the cross-section both in the angular and radial directions, and to occupy any length of the pipe span. A B-spline wavelet-based finite element method (BWFEM) that takes advantage of the localization properties of wavelets is invoked; thus utilizing its effectiveness in modeling of crack problems and local damages. The composite pipe was treated as beam elements that obey the Euler–Bernoulli beam theory. Unlike the conventional finite element method (FEM), the developed BWFEM uses fewer elements without compromising the accuracy. Numerical simulations are performed to demonstrate the accuracy and efficiency of the developed element through comparison with available results in the literature, as well as results obtained using ANSYS. Some benchmark solutions are obtained for the composite pipe with internal surface defects of different geometries.

Modal Analysis of Cracked Plate Using Interval B-Spline Wavelet Finite Element Method

2011 ◽  
Vol 199-200 ◽  
pp. 1287-1291
Author(s):  
Hui Fen Peng ◽  
Guang Wei Meng ◽  
Li Ming Zhou ◽  
Zhao Long Yang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Element Model ◽  
Mode Shapes ◽  
Plate Element ◽  
Spline Wavelet ◽  
B Spline ◽  
Cracked Plate ◽  
Wavelet Finite Element ◽  
Element Method

Aiming at the defects in describing stress field near the crack tip with traditional finite element method (TFEM), a new finite element method based on interval B-Spline wavelet (IBSW) is put forward, the displacement interpolation functions of plate element are constructed by using the scaling functions of IBSW, finite element model of cracked plate based on IBSW is established, and the stiffness matrixes of plate element is derived. The first four natural frequencies and mode shapes of the cracked plate are obtained by using interval B-Spline wavelet finite element (IBSWFE). Comparison of the calculated results with those by ANSYS shows that IBSWFE method can get higher calculation precision with less elements in dealing with engineering singularity problems.

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